Fully aromatic polyesters characterized by formation of anisotropic melts have been disclosed in a number of patents. These are generally spun at moderate molecular weight to form oriented fibers of low to moderate tensile strength. Subsequently, these as-spun fibers can be subjected to heat-treatment over fairly long periods of time as a result of which they increase in molecular weight and strengthen significantly but there is expense associated with such heat-treatment. When attempts are made to spin higher strength fibers directly from higher molecular weight polymers of this class of compositions, poor properties and excessive diameter fluctuations along the length of the filaments are encountered. By use of certain techniques, this invention permits spinning of a specified class of anisotropic melt-forming polyesters of higher molecular weight with consistent attainment of uniform higher strength fibers than have been previously attainable from such high molecular weight polymers.